Epistemological Obstacle  Siswa dalam Menyelesaikan Masalah Konsep Barisan dan Deret Aritmetika

Arma Wangsa; Ully Hidayati; Adis Almaida

doi:10.51574/jrip.v6i2.5665

Authors

Arma Wangsa Program Studi Pendidikan Matematika, Fakultas Keguruan dan Ilmu Pendidikan, Universitas Sembilanbelas November Kolaka, Kolaka, Indonesia https://orcid.org/0009-0003-5898-3484
Ully Hidayati Program Studi Pendidikan Matematika, Fakultas Keguruan dan Ilmu Pendidikan, Universitas Sembilanbelas November Kolaka, Kolaka, Indonesia https://orcid.org/0009-0006-3044-5707
Adis Almaida Program Studi Pendidikan Matematika, Fakultas Keguruan dan Ilmu Pendidikan, Universitas Sembilanbelas November Kolaka, Kolaka, Indonesia

Keywords:

Barisan dan Deret Aritmetika, Epistemological Obstacle, Masalah Kontekstual

Abstract

Siswa masih mengalami kesulitan dalam mengaplikasikan konsep barisan dan deret aritmetika pada masalah berbasis konteks, yang mengindikasikan terjadinya epistemological obstacle. Oleh karena itu, tujuan penelitian ini untuk menjelaskan epistemological obstacle siswa dalam menyelesaikan masalah pada konsep barisan dan deret aritmetika. Melalui pendekatan kualitatif deskriptif yang melibatkan 17 siswa kelas XI SMK jurusan Geologi Pertambangan. Dari subjek tersebut, secara purposive terpilih empat lembar kerja sebagai subjek yang merepresentasikan variasi pola jawaban, strategi, dan tingkat keberhasilan. Peneliti mengumpulkan data melalui tes diagnostik yang terdiri atas lima soal, meliputi dua soal non-kontekstual dan tiga soal kontekstual, serta wawancara semi-terstruktur untuk mengonfirmasi kemampuan siswa dalam menyelesaikan masalah. Data dianalisis menggunakan teknik flow model, meliputi: reduksi data, penyajian data, dan penarikan kesimpulan. Hasil penelitian menunjukkan bahwa siswa cenderung mampu menyelesaikan masalah non-kontekstual secara formal (U_n dan S_n) maupun secara intuisi menggunakan penjumlahan berulang, tetapi mengalami penurunan kemampuan pada masalah kontekstual. Analisis lembar kerja dan hasil wawancara menunjukkan bahwa siswa dapat menerapkan prosedur yang telah dipelajari secara mekanis, tatapi belum mampu mengidentifikasi konsep yang sesuai ketika konteks masalah berbeda dari pengalaman belajarnya. Temuan ini menunjukkan bahwa epistemological obstacle ditandai oleh ketidakmampuan mentransfer pengetahuan ketika konteks masalah mengalami perubahan. Kondisi tersebut mengakibatkan siswa mengalami kesulitan dalam memilih konsep dan menentukan strategi penyelesaian. Temuan penelitian ini menjadi landasan dalam mengembangkan strategi pembelajaran yang menekankan pemahaman konseptual dan kemampuan transfer pengetahuan dalam berbagai konteks masalah.

Downloads

Download data is not yet available.

References

Alpianto, A., Firdaus, A. M., & Husniati, A. (2026). The Effectiveness of Canva-Based Interactive Learning Media on Students’ Conceptual Understanding of Arithmetic Sequences. Journal of Mathematics, Science and Technology Education, 3(2), 45–56. https://doi.org/10.12973/jmste.3.2.45

Andzin, N. S., Sari, P. Y. P., Widodo, R. C., Sukowati, D. I., Indriastuti, S., & Nursyahidah, F. (2024). Arithmetic Sequences and Series Learning Using Realistic Mathematics Education Assisted by Augmented Reality. Jurnal Pendidikan Matematika, 18(1), 139–148. https://doi.org/10.22342/jpm.v18i1.pp139-148

Bangun, A. M. P., Imami, A. I., & Marlina, R. (2026). Mapping Epistemological Obstacles in Junior High School Students’ Statistical Word-Problem Solving: A Systematic Literature Review. Jurnal Didactical Mathematics, 8(2), 323–344. https://doi.org/10.31949/dm.v8i2.18712

Brousseau, G. (2002). The Didactical Contract: The Teacher, the Student and the Milieu. In Mathematics Education Library (Vol. 19, pp. 226–249). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47211-2_13

Chiasson, M., & Freiman, V. (2022). Rethinking the 21st-Century School: New Citizens’ Skills for the Digital Era and Their Interaction with Mathematics Teaching and Learning (pp. 69–107). https://doi.org/10.1007/978-3-031-10518-0_5

Danil C, F., Zulkardi, Z., Susanti, E., & Meryansumayeka, M. (2025). Design Learning Of Arithmetic Sequence Using Stair Context To Support Students’ Conceptual Understanding. Prima: Jurnal Pendidikan Matematika, 9(3), 520–536. https://doi.org/10.31000/prima.v9i3.12886

Deslis, D., & Desli, D. (2023). Does this Answer Make Sense? Primary School Students and Adults Judge the Reasonableness of Computational Results in Context-Based and Context-Free Mathematical Tasks. International Journal of Science and Mathematics Education, 21(1), 71–91. https://doi.org/10.1007/s10763-022-10250-0

Dewi, R., Riyadi, R., & Siswanto, S. (2022). Students’ Epistemological Obstacles in Statistical Problems. https://doi.org/10.2991/assehr.k.220403.026

Domu, I., & Mangelep, N. O. (2020). The Development of Students’ Learning Material on Arithmatic Sequence Using PMRI Approach. Proceedings of the International Joint Conference on Science and Engineering (IJCSE 2020). https://doi.org/10.2991/aer.k.201124.076

Fitriani, N., Sugiman, S., & Arfah, A. (2023). Didactical design of algebraic expression from a linear pattern with a realistic mathematics education approach. Jurnal Riset Pendidikan Matematika, 10(1), 1–16. https://doi.org/10.21831/jrpm.v10i1.55212

Hendriyanto, A., Suryadi, D., Juandi, D., Dahlan, J. A., Hidayat, R., Wardat, Y., Sahara, S., & Muhaimin, L. H. (2024). The didactic phenomenon: Deciphering students’ learning obstacles in set theory. Journal on Mathematics Education, 15(2), 517–544. https://doi.org/10.22342/jme.v15i2.pp517-544

Huberman, A. M., & Miles, M. B. (1983). Drawing valid meaning from qualitative data: Some techniques of data reduction and display. Quality & Quantity, 17(4), 281. https://doi.org/10.1007/BF00167541

Klau, K. Y., Siahaan, M. M. L., & Simarmata, J. E. (2020). An Identification of Conceptual and Procedural Understanding: Study on Preservice Secondary Mathematics Teacher. Al-Jabar : Jurnal Pendidikan Matematika, 11(2), 339–350. https://doi.org/10.24042/ajpm.v11i2.7310

Lestari, T. V. D., & Marsigit. (2020). Hypothetical learning trajectory and students’ understanding of the concepts of the arithmetic sequence. Journal of Physics: Conference Series, 1581(1), 012038. https://doi.org/10.1088/1742-6596/1581/1/012038

Maarif, S., Perbowo, K. S., & Kusharyadi, R. (2021). Depicting Epistemological Obstacles in Understanding the Concept of Sequence and Series. IndoMath: Indonesia Mathematics Education, 4(1), 66–80. https://doi.org/10.30738/indomath.v4i1.9339

Magfiroh, M., Prabawanto, S., & Rosjanuardi, R. (2024). Learning obstacle of students in geometrical sequence and series. KnE Social Sciences. https://doi.org/10.18502/kss.v9i13.15960

Marta Towe, M. (2026). Problem-Solving Ability In Arithmetic Sequences And Series Using Problem-Based Learning. Absis: Mathematics Education Journal, 8(1), 44–53. https://doi.org/10.32585/absis.v8i1.8178

Murniasih, T. R., Susiswo, S., Utami, A. D., Lanya, H., Putri, O. R. U., & Parameswari, P. (2024). Limit: Identification of student epistemological obstacles. 030011. https://doi.org/10.1063/5.0235275

Mutawah, M. A. Al, Thomas, R., Eid, A., Mahmoud, E. Y., & Fateel, M. J. (2019). Conceptual Understanding, Procedural Knowledge and Problem-Solving Skills in Mathematics: High School Graduates Work Analysis and Standpoints. International Journal of Education and Practice, 7(3), 258–273. https://doi.org/10.18488/journal.61.2019.73.258.273

Nurhikmayati, I., & Darhim. (2026). What are students’ obstacle in learning geometry? An analysis of students’ learning obstacles on geometry of cubes and cuboids. 020011. https://doi.org/10.1063/5.0330518

OECD. (2019). PISA 2018 Results Combined Executive Summaries Volume I, II & III. In PISA 2009 at a Glance: I, II & II. OECD Publishing. https://doi.org/10.1787/g222d18af-en

OECD. (2023). PISA 2022 Results (volume I). OECD Publications: Paris, France. https://doi.org/10.1787/53f23881-en

Pusat Asesmen Pendidikan. (2026). Statistik Nasional Rerata Nilai Per Mata Pelajaran. Kemendikdasmen Badan Kebijakan Pendidikan Dasar Dan Menengah Pusat Asesmen Pendidikan. https://tka.kemendikdasmen.go.id/hasiltka/

Rachma, A. A., Rosjanuardi, R., & Suhendra, S. (2022). Students’ mathematical obstacles in learning geometric sequences and series. 070058. https://doi.org/10.1063/5.0120129

Ruli, R. M., Juandi, D., Dahlan, J. A., & Maudy, S. Y. (2025). From Arithmetic to Algebra: Students’ Epistemological Obstacles. SJME (Supremum Journal of Mathematics Education), 9(2), 371–382. https://doi.org/10.35706/sjme.v9i2.205

Sebök, K., & Lensing, F. (2025, February). On the concept of epistemic obstacles and its significance to mathematics education (research). Theoretical Perspectives and Approaches in Mathematics Education Research. https://hal.science/hal-05283890v1

Siagian, M. D., Suryadi, D., Nurlaelah, E., & Prabawanto, S. (2022). Investigation of Secondary Students’ Epistemological Obstacles in the Inequality Concept. Mathematics Teaching-Research Journal, 106(4), 106–128. https://files.commons.gc.cuny.edu/wp-content/blogs.dir/34462/files/2024/07/06-Siagian.pdf

Sudirman, S., Kusumah, Y. S., Martadiputra, B. A. P., & Runisah. (2023). Epistemological Obstacle in 3D Geometry Thinking: Representation, Spatial Structuring, and Measurement. Pegem Journal of Education and Instruction, 13(4). https://doi.org/10.47750/pegegog.13.04.34

Wangsa, A., Rahayu, D. S., Wahdaniah, P., & Umasugi, S. M. (2026). Integrating popular digital contexts into realistic mathematics education: Designing a hypothetical learning trajectory for arithmetic sequences and series. Journal of Honai Math, 8(3), 481–495. https://journalfkipunipa.org/index.php/jhm/article/view/1038

Warli, D., Fatimah, S., Wicaksono, A., Kahar, M. J., Fajriani, F., & Deeteng, A. (2025). Exploration of student learning obstacles in solving propotional problems in junior high school. Al-Jabar : Jurnal Pendidikan Matematika, 16(1), 207–220. https://doi.org/10.24042/ajpm.v16i1.26478

Zhou, T., & Ogbonnaya, U. l. (2026). Application vs. non-application contexts in Euclidean geometry tasks in grades 10–12 South African mathematics textbooks. Desimal: Jurnal Matematika, 9(1), 70–83. https://doi.org/10.24042/djm.v9i1.29549